Complete the exercises below. For each of the following metals, write the electronic configuration of the atom and its 2+ ion: a. Mn. Draw the crystal-field energy-level diagram for the d orbitals of an octahedral complex, and show the placement of the d electrons for each 2+ ion, assuming a strong-field complex. How many unpaired electrons are there in each case? b. Ru. Draw the crystal-field energy-level diagram for the d orbitals of an octahedral complex, and show the placement of the d electrons for each 2+ ion, assuming a strong-field complex. How many unpaired electrons are there in each case? c. Rh. Draw the crystal-field energy-level diagram for the d orbitals of an octahedral complex, and show the placement of the d electrons for each 2+ ion, assuming a strong-field complex. How many unpaired electrons are there in each case?

Verified step by step guidance

1. Step 1: Determine the electronic configuration of the neutral atom for each metal. For Mn, the atomic number is 25, so the configuration is [Ar] 3d^5 4s^2. For Ru, the atomic number is 44, so the configuration is [Kr] 4d^7 5s^1. For Rh, the atomic number is 45, so the configuration is [Kr] 4d^8 5s^1.
2. Step 2: Write the electronic configuration for the 2+ ion by removing two electrons, typically from the outermost s orbital first, then from the d orbital if necessary. For Mn^2+, remove two electrons from 4s, resulting in [Ar] 3d^5. For Ru^2+, remove one electron from 5s and one from 4d, resulting in [Kr] 4d^6. For Rh^2+, remove one electron from 5s and one from 4d, resulting in [Kr] 4d^7.
3. Step 3: Draw the crystal-field energy-level diagram for an octahedral complex. In an octahedral field, the d orbitals split into two sets: the lower-energy t2g (dxy, dxz, dyz) and the higher-energy eg (dx2-y2, dz2) orbitals.
4. Step 4: Place the d electrons in the crystal-field diagram for each 2+ ion, assuming a strong-field complex. In a strong-field complex, electrons pair up in the lower-energy t2g orbitals before occupying the higher-energy eg orbitals. For Mn^2+ with 5 d electrons, fill the t2g orbitals first. For Ru^2+ with 6 d electrons, fill the t2g orbitals and start filling the eg orbitals. For Rh^2+ with 7 d electrons, fill the t2g orbitals and continue filling the eg orbitals.
5. Step 5: Count the number of unpaired electrons in each case. For Mn^2+, determine how many electrons remain unpaired in the t2g orbitals. For Ru^2+, check the pairing in both t2g and eg orbitals. For Rh^2+, assess the pairing in both t2g and eg orbitals to find the number of unpaired electrons.

Key Concepts

Electronic Configuration

Electronic configuration describes the distribution of electrons in an atom's orbitals. For transition metals, this involves filling the 3d and 4s orbitals. Understanding how to write the electronic configuration for both the neutral atom and its 2+ ion is crucial, as the loss of electrons typically occurs from the outermost shell, affecting the overall electron arrangement.

Crystal Field Theory

Crystal Field Theory (CFT) explains how the presence of ligands around a metal ion affects the energy levels of its d orbitals. In an octahedral complex, the d orbitals split into two energy levels: the lower-energy t2g and the higher-energy eg orbitals. This theory helps predict the arrangement of electrons in these orbitals and the resulting magnetic properties of the complex.

Unpaired Electrons and Magnetism

The number of unpaired electrons in an atom or ion determines its magnetic properties. Unpaired electrons contribute to paramagnetism, while paired electrons lead to diamagnetism. In the context of transition metal complexes, knowing how to identify unpaired electrons after applying CFT is essential for predicting the magnetic behavior of the complex.